94,836 research outputs found
Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity
We relate the structure factor in a system of
jammed hard spheres of number density to its complexity per particle
by the formula . We have verified this formula for
the case of jammed disks in a narrow channel, for which it is possible to find
and analytically. Hyperuniformity, which is the
vanishing of , will therefore not occur if the
complexity is nonzero. An example is given of a jammed state of hard disks in a
narrow channel which is hyperuniform when generated by dynamical rules that
produce a non-extensive complexity.Comment: 5 pages, 3 figure
Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
We use an exact transfer-matrix approach to compute the equilibrium
properties of a system of hard disks of diameter confined to a
two-dimensional channel of width at constant longitudinal
applied force. At this channel width, which is sufficient for
next-nearest-neighbor disks to interact, the system is known to have a great
many jammed states. Our calculations show that the longitudinal force
(pressure) extrapolates to infinity at a well-defined packing fraction
that is less than the maximum possible , the latter
corresponding to a buckled crystal. In this quasi-one-dimensional problem there
is no question of there being any \emph{real} divergence of the pressure at
. We give arguments that this avoided phase transition is a structural
feature -- the remnant in our narrow channel system of the hexatic to crystal
transition -- but that it has the phenomenology of the (avoided) ideal glass
transition. We identify a length scale as our equivalent of the
penetration length for amorphous order: In the channel system, it reaches a
maximum value of around at , which is larger than the
penetration lengths that have been reported for three dimensional systems. It
is argued that the -relaxation time would appear on extrapolation to
diverge in a Vogel-Fulcher manner as the packing fraction approaches .Comment: 17 pages, 16 figure
Disappearance of the de Almeida-Thouless line in six dimensions
We show that the Almeida-Thouless line in Ising spin glasses vanishes when
their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where
C is a constant of order unity. An equivalent result which could be checked by
simulations is given for the one-dimensional Ising spin glass with long-range
interactions. It is shown that replica symmetry breaking also stops as d -> 6.Comment: Additional text and one figure adde
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